Languages:

Related Data and Programs:

CUBE_ARBQ_RULE,
a C library which
returns quadrature rules,
with exactness up to total degree 15,
over the interior of the symmetric cube in 3D,
by Hong Xiao and Zydrunas Gimbutas.

CUBE_FELIPPA_RULE,
a C library which
returns the points and weights of a Felippa quadrature rule
over the interior of a cube in 3D.

GNUPLOT,
C programs which
illustrate how a program can write data and command files
so that gnuplot can create plots of the program results.

PYRAMID_FELIPPA_RULE,
a C library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a pyramid in 3D.

SQUARE_FELIPPA_RULE,
a C library which
returns the points and weights of a Felippa quadrature rule
over the interior of a square in 2D.

SQUARE_GRID,
a C library which
computes a grid of points
over the interior of a square in 2D.

SQUARE_INTEGRALS,
a C library which
returns the exact value of the integral of any monomial
over the interior of the unit square in 2D.

SQUARE_MONTE_CARLO,
a C library which
uses the Monte Carlo method to estimate the integral of a function
over the interior of the unit square in 2D.

SQUARE_SYMQ_RULE,
a C library which
returns efficient symmetric quadrature rules,
with exactness up to total degree 15,
over the interior of a symmetric square in 2D,
by Hong Xiao and Zydrunas Gimbutas.

STROUD,
a C library which
defines quadrature rules for a variety of M-dimensional regions,
including the interior of the square, cube and hypercube, the pyramid,
cone and ellipse, the hexagon, the M-dimensional octahedron,
the circle, sphere and hypersphere, the triangle, tetrahedron and simplex,
and the surface of the circle, sphere and hypersphere.

TETRAHEDRON_ARBQ_RULE,
a C library which
returns quadrature rules,
with exactness up to total degree 15,
over the interior of a tetrahedron in 3D,
by Hong Xiao and Zydrunas Gimbutas.

TETRAHEDRON_FELIPPA_RULE,
a C library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a tetrahedron in 3D.

TOMS886,
a C library which
defines the Padua points for interpolation in a 2D region,
including the rectangle, triangle, and ellipse,
by Marco Caliari, Stefano de Marchi, Marco Vianello.
This is a version of ACM TOMS algorithm 886.

TRIANGLE_FEKETE_RULE,
a C library which
defines Fekete rules for interpolation or quadrature
over the interior of a triangle in 2D.

TRIANGLE_FELIPPA_RULE,
a C library which
returns Felippa's quadratures rules for approximating integrals
over the interior of a triangle in 2D.

TRIANGLE_SYMQ_RULE,
a C library which
returns efficient symmetric quadrature rules,
with exactness up to total degree 50,
over the interior of an arbitrary triangle in 2D,
by Hong Xiao and Zydrunas Gimbutas.

WEDGE_FELIPPA_RULE,
a C library which
returns quadratures rules for approximating integrals
over the interior of the unit wedge in 3D.

Reference:

Hong Xiao, Zydrunas Gimbutas,
A numerical algorithm for the construction of efficient quadrature
rules in two and higher dimensions,
Computers and Mathematics with Applications,
Volume 59, 2010, pages 663-676.